The world — the whole Earth or human society as a whole; used to refer to the global or worldwide scope.
クリスマスは世界の多くの国で祝われている。
Christmas is celebrated in many countries around the world.
世界の人口は増加を続けている。
The world's population continues to increase.
彼女は世界を旅して多くの文化に触れた。
She traveled the world and experienced many cultures.
A sphere or circle — used to refer to a particular field, realm, or community (as in 'the world of fashion').
芸術の世界で成功するのは簡単ではない。
Succeeding in the world of art is not easy.
彼はスポーツの世界では有名なコーチだ。
He is a well-known coach in the sports world.
Used to indicate world-wide renown or scope (as in 'world-famous' or in compounds like '世界の〜'), often appears with the genitive particle 'の'.
彼は世界の舞台で活躍するピアニストだ。
He is a pianist who performs on the world stage.
その映画監督は世界に名を知られている。
That film director is known worldwide.
In Buddhist (and related) contexts: a realm or sphere governed by a particular Buddha; a technical/religious sense of 'world'.
仏教では『世界』という語が六道や浄土などの区分を指すことがある。
In Buddhism, the term 'world' may refer to divisions such as the six realms or Pure Lands.